Enter any combination of known sides and angles to solve a triangle completely: area, perimeter, all angles, all sides, altitudes, inradius and circumradius.
How to use this calculator
Select the combination of known measurements: three sides (SSS), two sides and the angle between them (SAS), two angles and the side between them (ASA), or two angles and a non-included side (AAS).
Enter the known values in the fields shown.
All remaining sides, angles, area, perimeter, and altitudes appear instantly.
For right triangles, use the dedicated Right Triangle Calculator for additional outputs.
Formula & method
Law of Cosines & Heron's Formula
c² = a² + b² − 2ab·cos(C) · Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2
Law of Cosines applies for SSS/SAS. Law of Sines (a/sin A = b/sin B = c/sin C) applies for ASA/AAS. Heron's formula requires all three sides.
Example
Triangle with sides 3, 4, 5: s = 6, Area = √(6·3·2·1) = √36 = 6. Angles: A = 36.87°, B = 53.13°, C = 90°.
Key insights
For a 3-4-5 right triangle, the area is 6 square units and the hypotenuse is exactly 5 — the simplest Pythagorean triple.
The Law of Cosines generalizes the Pythagorean theorem: c² = a² + b² − 2ab·cos(C).
The triangle inequality requires every side to be strictly less than the sum of the other two.
An equilateral triangle with side s has area (√3/4)s² and all three 60° angles.
The inradius r = Area / s where s is the semi-perimeter; the circumradius R = abc / (4·Area).
How to interpret your result
Area (Heron's formula)
Computed from the semi-perimeter s and all three sides: Area = √(s(s−a)(s−b)(s−c)). Works for any triangle once all sides are known.
Triangle type
Classified by sides (scalene, isosceles, equilateral) and by largest angle (acute, right, obtuse). This affects how area and height distribute across the triangle.
Height (altitude)
The altitude to side a is hₐ = 2·Area / a. In architecture and surveying, altitudes are used to measure effective perpendicular distances.
Frequently asked questions
Can I solve a triangle with only two sides and no angle?
No — you need at least one angle or you cannot uniquely determine the triangle. Two sides alone (SS) give infinite solutions.
What is the triangle inequality?
Any side must be strictly less than the sum of the other two. If not satisfied, no triangle exists.
How is this different from the Right Triangle Calculator?
This calculator handles all triangle types (scalene, isosceles, equilateral, obtuse) via SSS/SAS/ASA/AAS. The Right Triangle Calculator specializes in right-angled triangles with hypotenuse and Pythagorean triple detection.
Related calculators
Right Triangle Calculator — Solve a right triangle from any two known values — legs, hypotenuse, or an angle — using the Pythagorean theorem.
Area Calculator — Calculate the area and perimeter of rectangles, squares, circles, triangles, trapezoids, ellipses and parallelograms.